I re-flowed the terminals where I wasn't getting any resistance. And I ran some more tests.
Those same terminals (31, 36, and B2) are STILL not giving me any reading. At all. (Any thoughts on this?)
I tried the pot as suggested. With the bottom center pin I can't get a consistent tracking of numbers as I turn the knob. It cuts out at a couple points, but only for a split second and then starts tracking. Not sure if this is a sign of something wrong.
I plugged it back in and turned it on and it's fine. No screeching. Yet. I do, however, hear some slight noise with volume pot turned all the way up. But the noise is very slight, and I doubt I could hear it with music playing.
For now I will simply let it be. If it starts screeching or squealing again, I'll post back.